The acceleration of coronal mass ejections (CMEs) is examined focusing on three specific questions raised by observations: (1) what determines the height beyond which a CME exhibits no rapid acceleration, (2) why is the main acceleration of CMEs typically limited to below 2--3 solar radii, and (3) are distinct mechanisms required to explain the apparent bimodal distribution of speed-height profiles. Using a theoretical model of CMEs based on a three-dimensional (3-D) magnetic flux rope, it is shown that the acceleration of CMEs exhibits a universal scaling law characterized by the critical height Z* = Sf/2 such that maximum acceleration is attained shortly after height Z of the flux-rope apex exceeds Z*, where Sf is the footpoint separation distance. Theoretical analysis and observed CME dynamics show two distinct phases of acceleration: the main and residual acceleration phases. The main acceleration phase occurs for apex height Z ≤ Zm, where Zm is found to be ≃3 Z*, and the residual acceleration phase corresponds to Z > Zm. Thus the observed acceleration profile can be directly related to Sf. These results are explained in terms of the 3-D geometry of a flux rope, its inductive properties, and the Lorentz self-force. We have also constructed ensembles of flux-rope profiles corresponding to varying amounts and durations of poloidal flux injection. We find that the resulting distribution of model speed-height profiles is similar to that observed if an upper limit on the amount of injected flux is imposed. One mechanism is sufficient to account for the observed properties and distribution of CME acceleration. The theory is quantitatively tested against observed CMEs.